This PDF is a selection from an out-of-print volume from the National Bureau of Economic Research Volume Title: Explorations in Economic Research, Volume 3, number 3 Volume Author/Editor: NBER Volume Publisher: NBER Volume URL: http://www.nber.org/books/sarg76-1 Publication Date: 1976 Chapter Title: Interest Rates and Expected Inflation: A Selective Summary of Recent Research Chapter Author: Thomas J. Sargent Chapter URL: http://www.nber.org/chapters/c9082 Chapter pages in book: (p. 1 - 23) 1 THOMAS J. SARGENT University of Minnesota Interest Rates and Expected Inflation: A Selective Summary of Recent Research ABSTRACT: This paper summarizes the macroeconomics underlying Irving Fisher's theory about tile impact of expected inflation on nomi­ nal interest rates. Two sets of restrictions on a standard macroeconomic model are considered, each of which is sufficient to iniplv Fisher's theory. The first is a set of restrictions on the slopes of the IS and LM curves, while the second is a restriction on the way expectations are formed. Selected recent empirical work is also reviewed, and its implications for the effect of inflation on interest rates and other macroeconomic issues are discussed. INTRODUCTION This article is designed to pull together and summarize recent work by a few others and myself on the relationship between nominal interest rates and expected inflation.' The topic has received much attention in recent years, no doubt as a consequence of the high inflation rates and high interest rates experienced by Western economies since the mid-1960s. NOTE: In this paper I Summarize the results of research 1 conducted as part of the National Bureaus study of the effects of inflation, for which financing has been provided by a grait from the American life Insurance Association Heiptul coinrnents on earlier eriiins of 'his p,irx'r serv marIe ti PhillipCagan arid l)y the mnibrirs Ut the stall reading Committee: Michael R. Darbv, ohn Eiritner, and Rohet J. SmIler. Thanks arE' also due he nic'nihers of the Board reading corpnhitte. Gardner Ackley. lames I. O'Lear, and Eli Shapiro, for their services. Ester Mokosvltz provided able editorial assistance. 303 S 304 Thomas I. Sargent Most work on the topic has in one form or another been based on Irving Fisher's famous theory about interest and inflation (Fisher 1930). That theory holds that an increase in the rate of inflation expected by the public leads to an equivalent increase in the nominal rate of interest, thereby ieaviiig the real rate of interest unaltered. A central message of Keynes's General Theory is that the tlieoiy of interest is macroeconomic in content. It was because of its macroeconomic implications that Keynes (1936) objected to Irving Fisher's theory about the effect of expected inflation on nominal interest rates. Fisher's "classical" in its theory is macroeconomic content, being in the nature of a "neu­ trality" result, and to deduce it requires making a batch of classical assumptions about the way the economy is put together. It was those assumptions and their policy implications that no doubt Prompted Keynes to take exception to Fisher's theory. Unfortunately Keynes's message has been disregarded in much of thy recent empirical work that has purported to enìbrace Fisher's theory. "Interest rate equations" have been estimated that cannot he interpreted either as structural equations or reduced form equations of theory.2 Much of this macroeconomic work goes astray precisely because it fails to recognize the macroeconomic content of Fisher's theory and the tives to it. For that alterna­ reason, this paper begins in section 1 with a review of the macroeconomic theory underlying Fisher's static proposition that a jump in expected inflation will be matched by mediate jump in the an equivalent and im­ nominal rate of interest. Two alternative assumptions are entertained about the way expectations are formed. First, that expectations it is assumed are formed in an ad hoc, "adaptive" manner, and so is a certain distributed lag of past actual rates of inflation. assumption is used in most This kind of empirical work. The alternative assumption is that expectations "rational" in Muth's (1961) sense, and so equal the predictions of economic theory. My exposition is in terms of a noiistochas tic model; in that case, the natural way to represent rational expectations is to assume perfect foresight. Individuals are assumed the actual (right-hand) accurately to perceive time derivative of the log of the price level, and this is taken to be their expected rate of inflation.3 It happens that it makes a great difference how expectations are assumed with ad hoc, adaptive to be formed. In the model expectations, Fisher's Static under certain highly proposition emerges only restrictive conditions on the values assumed by the model s parameters, in particular and LM curves, restrictions on the relative slopes of the IS On the other hand, with rational restrictions are required. expectations, no such While for purposes of simplicity my exposition of in terms of a nonsfochastic rational expectations is model, it should be noted that a more plausible, stochastic version of the theory has been written down (Sargent 1973), one L Interest Rates and Inflation 305 that is "classical" in some respects, including the incorporation of a version of Fisher's static proposition, but is "Keynesian" in other respects, such as its ability to rationalize the existence of business cycles that are caused by fluctuations in aggregate demand. It is my view that such stochastic classical models provide the most robust foundations for Fisher's theory and certain other classical propositions. The rionstochastic version of the model in this paper captures the essence of what is going on in the rational expectations model, but fails adequately to indicate how models of this kind can be compatible with recurrent business cycles. In any event, the models described in this paper do show that wide-ranging implications flow from replacing the assumption of adaptive expectations with that of rational expectations. Section II of the paper contains a short and very selective review of some empirical work that has been done on the topic. Most researchers have assumed some form of adaptive or fixed-weight--autoregressive expecta­ tions. Unfortunately, as will be shown, most models incorporating such an assumption have more parameters than can be estimated from the data, and so are not econometrically identifiable. The usual identifying restric­ tion, that a certain sum of coefficients equals unity, is arbitrary and cannot be defended on any general principle. The most plausible way to crack this identification problem is to assume that expectations ar rational. That is the approach taken in studies by Shiller (1972) and Fama (1973). They employ the simplest version of Fisher's theory and use the hypothesis that expectations are "rational" to deduce testable restrictions. Theirs is the most serious empirical work on the topic yet done. [I] THE MACROSTATICS OF FISHER'S PROPOSITION In this section I review the statics of Fisher's theory within the context of a standard one-sector Keynesian macroeconomic model. Time is continuous. I assume an aggregate production function that is linearly homogeneous in employment, N, and capital, K, and write it as Y/K = [(N/K), or y = 1(X), i'(X) > 0, f"(A) < 0 where y = Y/K and X = N/K; Y is real GNP, i.e., output per unit of time. The marginal product condition for employment can be written as - = PR) which expresses the assumption that employers hire workers at each moment until the real wage equals the marginal product of employment. Here w is the money wage, and P is the price level, i.e., the price of the one good in the model. a 306 fhonia', I. Slrgerit The Keynesian investnient schedule makes the rate of capital accuniula tion vary directly with the gap between the marginal product of capital, f() kf'R), and the real cost of capital, r -F () Here r is the instantaneous rate of interest, is the instclntaneous deprecia­ tion rate, and ir is the instantaneous expected rate of intlation. Consumption, C, is assumed to be a linear and proportional function of disposable income, Y T K K K K or c = z(y - - , where c = C/K, i = TIK. Here T is the rate of collections net of transfers, and tax z is the inatinal propensity to consume. The national income identity is where g = C!K, C being government purchases of goods and unit of tinie. services per Portfolio equilibrium is described by () -_L = m(r. ) m < 0, 1fl> 0 where Al is the supply of money. I posit that the evolution of money wages is governed by the Friedman- Phelps version 01 the Phillips curve 11(NN) + IT; h' > 0; h(;) = 0 where N3 is the full-employment labor supply and D is the right-hand derivative Operator. The time full-employment labor supply is assumed for normal hours worked, normal to allow turnover rates, etc. Consequently employment in man-years can exceed the full-employment labor supply if aggregate demand is high enough and if there is sufficient rigidity in the money wage. Given n-, equation 7 depicts employment relative to a trade-off bet'eeii the rate of the labor supply and the rate of increase in ir shifts the Phillips wage inflation. An increase. curve upward by the amount of that I assume that the labor supply is exogenous and is governed b' (3) \"( = '(f*" where n is the proportionate rate of growth of the labor The model is completed by specifying supply. the way in which expectations of interest Rates and Inflation 307 inflation are formed.